While looking at different power amps I noticed on quite a few of them that they had both balanced and unbalanced connectors. What is the difference/advantage of either?

Google is your friend. Below is one of thousands of results that may help.

http://www.bluejeanscable.com/articles/balanced.htm

Micah, if the sending unit has a balanced output and the receiving unit a balanced input then a cable can be used to connect them which has two central conductors rather than one. The signals are sent out in opposite polarity on the conductors and are then reversed again by the input device, resulting in the cancellation of interference that impinged equally on the two conductors. This is particularly useful in professional applications where long runs in areas with high interference are often involved. In typical home applications the interference rejection of unbalanced connections using regular shielded coaxial cable is sufficient.

Ah Sirquack what a coincidence that your example came from Blue Jeans Cable. This is the company I was looking at going with due in part to the fact that it uses Belden cable which is manufactured right here in my home town of Richmond, Indiana.

Upon further investigation my Denon doesn't have balanced outputs, so the point is moot.

Many receivers don't, my 2805 does not either.